A naïve implementation of \(k\) -core iteratively deletes vertices whose degree falls below a \(k\) , until it deletes all vertices from the graph. The implementation has a computational complexity of \(\mathcal {O}(m\log {}n)\) , where \(m\)  and \(n\)  are the number of edges and vertices in the network, respectively. Batagelj and Zaversnik reduce the complexity to \(\mathcal {O}(m+n)\)  by keeping an in-memory array of all possible degree values and keeping track of bin boundaries [1]}.
